scholarly journals Blow-up for the 3-dimensional axially symmetric harmonic map flow into \begin{document}$ S^2 $\end{document}

2019 ◽  
Vol 39 (12) ◽  
pp. 6913-6943
Author(s):  
Juan Dávila ◽  
◽  
Manuel Del Pino ◽  
Catalina Pesce ◽  
Juncheng Wei ◽  
...  
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Axially Symmetric ◽  
3 Dimensional ◽  
Harmonic Map Flow

Infinite time blow-up for half-harmonic map flow from R into S1

2021 ◽  
Vol 143 (4) ◽  
pp. 1261-1335
Author(s):  
Yannick Sire ◽  
Juncheng Wei ◽  
Youquan Zheng
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Infinite Time ◽  
Harmonic Map Flow

scholarly journals Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
James Kohout ◽  
Melanie Rupflin ◽  
Peter M. Topping
Keyword(s):  
Constant Curvature ◽  
Harmonic Map ◽  
Gradient Flow ◽  
Minimal Immersion ◽  
Curvature Surface ◽  
Previous Theory ◽  
Target Manifold ◽  
Harmonic Map Flow

AbstractThe harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched minimal immersion, but only at a sequence of times converging to infinity, and only after pulling back by a sequence of diffeomorphisms. In this paper, we investigate whether it is necessary to pull back by these diffeomorphisms, and whether the convergence is uniform as {t\to\infty}.

scholarly journals Transition of blow-up mechanisms in k-equivariant harmonic map heat flow

Nonlinearity ◽  
2020 ◽  
Vol 33 (6) ◽  
pp. 2756-2796
Author(s):  
Paweł Biernat ◽  
Yukihiro Seki
Keyword(s):  
Heat Flow ◽  
Blow Up ◽  
Harmonic Map ◽  
Harmonic Map Heat Flow

scholarly journals Moving mesh for the axisymmetric harmonic map flow

2005 ◽  
Vol 39 (4) ◽  
pp. 781-796
Author(s):  
Benoit Merlet ◽  
Morgan Pierre
Keyword(s):  
Harmonic Map ◽  
Moving Mesh ◽  
Harmonic Map Flow

scholarly journals Asymptotics of the Teichmüller harmonic map flow

2013 ◽  
Vol 244 ◽  
pp. 874-893 ◽  
Author(s):  
Melanie Rupflin ◽  
Peter M. Topping ◽  
Miaomiao Zhu
Keyword(s):  
Harmonic Map ◽  
Harmonic Map Flow

scholarly journals A global weak solution to the Lorentzian harmonic map flow

2019 ◽  
Vol 63 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Xiaoli Han ◽  
Lei Liu ◽  
Liang Zhao
Keyword(s):  
Weak Solution ◽  
Harmonic Map ◽  
Global Weak Solution ◽  
Harmonic Map Flow
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